

from __future__ import annotations



class        A__:
						"""simple docstring"""






						def __init__(    self  ,      _lowercase    )     -> None:
									a_						:						Optional[int] 							= order

									# a_{0} ... a_{k}
									a_						:						Union[str, Any] 							= [1.0] + [0.0] * order
									# b_{0} ... b_{k}
									a_						:						Optional[Any] 							= [1.0] + [0.0] * order

									# x[n-1] ... x[n-k]
									a_						:						Dict 							= [0.0] * self.order
									# y[n-1] ... y[n-k]
									a_						:						Tuple 							= [0.0] * self.order





						def 			UpperCamelCase__					(    self  ,      _lowercase  ,      _lowercase    )     -> None:
									if len(_lowercase    ) < self.order:
												a_						:						str 							= [1.0, *a_coeffs]

									if len(_lowercase    ) != self.order + 1:
												a_						:						List[Any] 							= (
												    F'''Expected a_coeffs to have {self.order + 1} elements '''
												    F'''for {self.order}-order filter, got {len(_lowercase    )}'''
												)
												raise ValueError(_lowercase    )

									if len(_lowercase    ) != self.order + 1:
												a_						:						Any 							= (
												    F'''Expected b_coeffs to have {self.order + 1} elements '''
												    F'''for {self.order}-order filter, got {len(_lowercase    )}'''
												)
												raise ValueError(_lowercase    )

									a_						:						str 							= a_coeffs
									a_						:						Tuple 							= b_coeffs





						def 			UpperCamelCase__					(    self  ,      _lowercase    )     -> float:
									a_						:						str 							= 0.0

									# Start at index 1 and do index 0 at the end.
									for i in range(1  ,      self.order + 1    ):
												result += (
												    self.b_coeffs[i] * self.input_history[i - 1]
												    - self.a_coeffs[i] * self.output_history[i - 1]
												)

									a_						:						Optional[int] 							= (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

									a_						:						Any 							= self.input_history[:-1]
									a_						:						int 							= self.output_history[:-1]

									a_						:						Optional[int] 							= sample
									a_						:						List[Any] 							= result

									return result





from random import randint
from tempfile import TemporaryFile

import numpy as np


def 					_UpperCAmelCase				(						a__  ,	a__  ,	a__):

			'''simple docstring'''



			a_						:						List[Any] 							= 0
			if start < end:
						a_						:						Dict 							= randint(a__  ,	a__)
						a_						:						List[str] 							= a[end]
						a_						:						Tuple 							= a[pivot]
						a_						:						Tuple 							= temp

						a_							,					a_						:						List[Any] 							= _in_place_partition(a__  ,	a__  ,	a__)
						count += _in_place_quick_sort(a__  ,	a__  ,	p - 1)
						count += _in_place_quick_sort(a__  ,	p + 1  ,	a__)
			return count


def 					_UpperCAmelCase				(						a__  ,	a__  ,	a__):

			'''simple docstring'''



			a_						:						Optional[int] 							= 0
			a_						:						Union[str, Any] 							= randint(a__  ,	a__)
			a_						:						Union[str, Any] 							= a[end]
			a_						:						Any 							= a[pivot]
			a_						:						Any 							= temp
			a_						:						int 							= start - 1
			for index in range(a__  ,	a__):
						count += 1
						if a[index] < a[end]:  # check if current val is less than pivot value
									a_						:						str 							= new_pivot_index + 1
									a_						:						Optional[Any] 							= a[new_pivot_index]
									a_						:						str 							= a[index]
									a_						:						Union[str, Any] 							= temp

			a_						:						Union[str, Any] 							= a[new_pivot_index + 1]
			a_						:						Tuple 							= a[end]
			a_						:						Any 							= temp
			return new_pivot_index + 1, count


__snake_case				:      Union[str, Any]   		=			TemporaryFile()
__snake_case				:      Dict   		=			1_00  # 1000 elements are to be sorted


__snake_case		, __snake_case				:      int   		=			0, 1  # mean and standard deviation
__snake_case				:      Tuple   		=			np.random.normal(mu, sigma, p)
np.save(outfile, X)
print("""The array is""")
print(X)


outfile.seek(0)  # using the same array
__snake_case				:      str   		=			np.load(outfile)
__snake_case				:      Dict   		=			len(M) - 1
__snake_case				:      Dict   		=			_in_place_quick_sort(M, 0, r)

print(
    """No of Comparisons for 100 elements selected from a standard normal distribution"""
    """is :"""
)



print(z)


